Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$5.00$, and bags of cookies cost $$3.50$, and sales equaled $$24.00$ in total. There were $2$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${5x+3.5y = 24}$ ${y = x+2}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+2}$ for $y$ in the first equation. ${5x + 3.5}{(x+2)}{= 24}$ Simplify and solve for $x$ $ 5x+3.5x + 7 = 24 $ $ 8.5x+7 = 24 $ $ 8.5x = 17 $ $ x = \dfrac{17}{8.5} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+2}$ to find $y$ ${y = }{(2)}{ + 2}$ ${y = 4}$ You can also plug ${x = 2}$ into $ {5x+3.5y = 24}$ and get the same answer for $y$ ${5}{(2)}{ + 3.5y = 24}$ ${y = 4}$ $2$ bags of candy and $4$ bags of cookies were sold.